Pershing Square, Ackman's $10 billion hedge fund, is the largest shareholder in J.C. Penney . He told the audience at the CNBC and Institutional InvestorDelivering Alpha conference that he believes that the department store chain has the biggest potential upside of any company in Pershing Square's portfolio.

"We can make 15 times our money," Ackman said

Ackman described the companies recent setbacks as "a PR problem."

Ackman also stood by Ron Johnson, the former Apple executive Ackman recruited to run J.C. Penney.

Johnson has come under criticism following a first-quarter decline in same-store sales that far exceeded what Wall Street expected.

"He was a genius when we hired him. Now people think he's an idiot. A year or two from now people will think he's a genius again," Ackman said.